Most of the US researchers who do CASP are funded by NIH or NSF. Some are funded by private foundations, or are independently wealthy. Typically, as a "principal investigator" (postdoc, professor, scientist at a national lab) you write a proposal saying "here's my preivous work, here's the next obvious step, plz give monies so I can feed the dean's fund and pay for my grad students to manage my modest closet cluster".
A group of your competitors then trashes your proposal in a group and if you've properly massaged the right backs, you get a pittance, which permits you to struggle to keep up with all your promises.